B737-700 CREW DID NOT DETECT A LARGE TKOF GROSS WT ERROR IN THE LOAD MANIFEST.

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INADEQUATE LOAD SHEET COMPUTATIONS. AFTER TKOF; WE WERE TOLD TO CONTACT OPS BY THE TWR CTLR. WE CONTACTED OPS AND WERE GIVEN A NEW ZERO FUEL WT AND TKOF WT. IT TOOK A FEW SECONDS TO REALIZE THAT WE WERE 24000 LBS HEAVIER THAN LOAD SHEET COMPUTATIONS AND THAT WE OVERLOOKED A BIG MISTAKE ON THE LOAD SHEET. WE CALCULATED V1; VR; V2 TO BE 112 KTS; 112 KTS; 118 KTS. THE ACTUAL SPDS SHOULD HAVE BEEN 128 KTS; 128 KTS; 132 KTS. THE MISTAKE ON THE LOAD SHEET WAS THAT THE 4 WTS (PAX WT; FORWARD HOLD WT; AFT HOLD WT; AND OPERATIONAL WT) WERE NOT ADDED TOGETHER. THE AGENT ADDED AN ADJUSTMENT FOR 3 BAGS (100 LBS) AND ENTERED IT IN THE ZERO FUEL WT BOX. HE THEN ADDED THIS ADJUSTMENT TO THE OPERATIONAL WT AND ENTERED THIS IN THE ADJUSTMENT BOX. I ALWAYS REVIEW THE LOAD SHEET TO CHK FOR THE 10000 LB MISTAKE AGENTS OFTEN MAKE IN CARRYING THE NUMBERS WHEN DOING THE MATH. I DID REVIEW THIS LOAD SHEET. I DID THE PERFORMANCE BECAUSE THE FO WAS OCCUPIED WITH SOMETHING ELSE. LOOKING BACK; I DON'T KNOW HOW I OVERLOOKED THIS. MY ONLY EXPLANATION IS THE MATH UP TOP LOOKED COMPLETE BECAUSE ALL THE BOXES WERE FILLED. I SHOULD HAVE COMPARED THE PLANNED ZERO FUEL WT AND PLANNED TKOF WT WITH THOSE ON THE LOAD SHEET. A RESOLUTION FOR THIS MIGHT BE TO HAVE BOXES ON THE LOAD SHEET WHERE THE AGENT CAN ENTER PLANNED ZERO FUEL WT AND TKOF WT BEFORE THE FLT SO THE AGENT AND THE FLT CREW HAVE A QUICK CHK COMPARISON DURING THE HEAT OF THE MOMENT; PUSHBACK! ANOTHER SOLUTION IS TO TAKE OUT THE HUMAN FACTOR OF DOING THE MATH. SUPPLEMENTAL INFO FROM ACN 571421: JUST PRIOR TO PUSHBACK; WITH 5 MINS TO GO; THE CAPT WAS DOING THE OPC FOR THE TKOF TO HELP ME OUT. I ASSUMED THE OPC AND WT SHEET WERE CORRECT AND FAILED TO CHK. WE TAXIED OUT AND TOOK OFF ON RWY 30R. AFTER LIFTOFF AND AS WE WERE TOLD TO SWITCH TO DEP; TWR TOLD US THAT OUR OPS WANTED TO SPEAK TO US. I WAS FLYING AND WHEN THE FLAPS WERE RAISED TO 1 DEG WE WERE IMMEDIATELY IN THE YELLOW ARC ON THE AIRSPD INDICATOR. I PUSHED THE NOSE OVER AND ACCELERATED RAPIDLY. THE REST OF THE DEP WAS UNEVENTFUL. AFTER THE CAPT CONTACTED OPS; WE WERE BOTH SHOCKED TO FIND OUR ACTUAL TKOF WT WAS 24000 LBS HIGHER! THE NUMBERS: WHAT WE TOOK OFF WITH -- ZERO FUEL WT WAS 83763 LBS. TKOF WT WAS 102856 LBS. V1: 112 KTS; VR: 112 KTS; V2: 118 KTS. ACTUAL -- ZERO FUEL WT WAS 102856 LBS; TKOF WT WAS 127059 LBS; V1: 128 KTS; VR: 128 KTS; V2: 132 KTS. AS YOU CAN SEE; THE PAX WT OF 22600 LBS WAS NEVER ADDED TO ZERO FUEL WT. WE BOTH SHOULD HAVE THOUGHT 112 KTS AND 118 KTS WERE SLOW FOR OUR WT IN ADDITION TO DOUBLECHKING LOAD SHEET. FROM NOW ON; I WILL CHK LOAD SHEET AGAINST RELEASE WT.